1. Basic Gates and Functions
Introduction
Boolean functions may be practically implemented by using electronic gates. The
following points are important to understand.
Electronic gates require a power supply.
Gate INPUTS are driven by voltages having two nominal values,
e.g. 0V and 5V representing logic 0 and logic 1 respectively.
The OUTPUT of a gate provides two nominal values of voltage
only, e.g. 0V and 5V representing logic 0 and logic 1 respectively.
In general, there is only one output to a logic gate except in some
special cases.
There is always a time delay between an input being applied and
the output responding.
Logic gates
Digital systems are said to be constructed by using logic gates. These gates are the
AND, OR, NOT, NAND, NOR, EXOR and EXNOR gates. The basic operations are
described below with the aid of truth tables.
AND gate
The AND gate is an electronic circuit that gives a high output (1) only if all its inputs
are high. A dot (.) is used to show the AND operation i.e. A.B. Bear in mind that this
dot is sometimes omitted i.e. AB
OR gate
The OR gate is an electronic circuit that gives a high output (1) if one or more of its
inputs are high. A plus (+) is used to show the OR operation.
2. NOT gate
The NOT gate is an electronic circuit that produces an inverted version of the input at
its output. It is also known as an inverter. If the input variable is A, the inverted
output is known as NOT A. This is also shown as A', or A with a bar over the top, as
shown at the outputs. The diagrams below show two ways that the NAND logic gate
can be configured to produce a NOT gate. It can also be done using NOR logic gates
in the same way.
NAND gate
This is a NOT-AND gate which is equal to an AND gate followed by a NOT gate.
The outputs of all NAND gates are high if any of the inputs are low. The symbol is an
AND gate with a small circle on the output. The small circle represents inversion.
NOR gate
This is a NOT-OR gate which is equal to an OR gate followed by a NOT gate. The
outputs of all NOR gates are low if any of the inputs are high.
The symbol is an OR gate with a small circle on the output. The small circle
represents inversion.
3. EXOR gate
The 'Exclusive-OR' gate is a circuit which will give a high output if either, but not
both, of its two inputs are high. An encircled plus sign ( ) is used to show the EOR
operation.
EXNOR gate
The 'Exclusive-NOR' gate circuit does the opposite to the EOR gate. It will give a
low output if either, but not both, of its two inputs are high. The symbol is an EXOR
gate with a small circle on the output. The small circle represents inversion.
The NAND and NOR gates are called universal functions since with either one the
AND and OR functions and NOT can be generated.
Note:
A function in sum of products form can be implemented using NAND gates by
replacing all AND and OR gates by NAND gates.
A function in product of sums form can be implemented using NOR gates by
replacing all AND and OR gates by NOR gates.
4. Table 1: Logic gate symbols
Table 2 is a summary truth table of the input/output combinations for the NOT gate
together with all possible input/output combinations for the other gate functions. Also
note that a truth table with 'n' inputs has 2n rows. You can compare the outputs of
different gates.
Table 2: Logic gates representation using the Truth table
